Acronym pabidrid, J80
Name parabidiminished rhombicosidodecahedron
 
 © ©    ©
Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figures [4,5,10], [3,4,5,4]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
  • between {4} and {10}:   arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474°
  • between {5} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Confer
uniform relative:
srid  
related Johnson solids:
pecu   dirid  
general polytopal classes:
Johnson solids  
External
links
wikipedia   mathworld   quickfur

Incidence matrix according to Dynkin symbol

xxFofx5xfoFxx&#xt   → height(1,2) = height(5,6) = sqrt[(5+sqrt(5))/10] = 0.850651
                      height(2,3) = height(4,5) = sqrt[(5-sqrt(5))/10] = 0.525731
                      height(3,4) = sqrt[(5-2 sqrt(5))/5] = 0.324920

o.....5o.....     | 10  * * *  *  * | 1 1  1 0  0  0  0  0 0  0 0 0 | 1 1 1 0  0 0 0 0 0  at top {10}
.o....5.o....     |  * 10 * *  *  * | 0 0  1 1  1  1  0  0 0  0 0 0 | 0 1 1 1  1 0 0 0 0
..o...5..o...     |  *  * 5 *  *  * | 0 0  0 0  2  0  2  0 0  0 0 0 | 0 0 1 0  2 1 0 0 0
...o..5...o..     |  *  * * 5  *  * | 0 0  0 0  0  2  0  2 0  0 0 0 | 0 0 0 1  2 0 1 0 0
....o.5....o.     |  *  * * * 10  * | 0 0  0 0  0  0  1  1 1  1 0 0 | 0 0 0 0  1 1 1 1 0
.....o5.....o     |  *  * * *  * 10 | 0 0  0 0  0  0  0  0 0  1 1 1 | 0 0 0 0  0 0 1 1 1  at bottom {10}
------------------+-----------------+-------------------------------+-------------------
x..... ......     |  2  0 0 0  0  0 | 5 *  * *  *  *  *  * *  * * * | 1 1 0 0  0 0 0 0 0  {4},{10}-join
...... x.....     |  2  0 0 0  0  0 | * 5  * *  *  *  *  * *  * * * | 1 0 1 0  0 0 0 0 0  {5},{10}-join
oo....5oo....&#x  |  1  1 0 0  0  0 | * * 10 *  *  *  *  * *  * * * | 0 1 1 0  0 0 0 0 0
.x.... ......     |  0  2 0 0  0  0 | * *  * 5  *  *  *  * *  * * * | 0 1 0 1  0 0 0 0 0
.oo...5.oo...&#x  |  0  1 1 0  0  0 | * *  * * 10  *  *  * *  * * * | 0 0 1 0  1 0 0 0 0
.o.o..5.o.o..&#x  |  0  1 0 1  0  0 | * *  * *  * 10  *  * *  * * * | 0 0 0 1  1 0 0 0 0
..o.o.5..o.o.&#x  |  0  0 1 0  1  0 | * *  * *  *  * 10  * *  * * * | 0 0 0 0  1 1 0 0 0
...oo.5...oo.&#x  |  0  0 0 1  1  0 | * *  * *  *  *  * 10 *  * * * | 0 0 0 0  1 0 1 0 0
...... ....x.     |  0  0 0 0  2  0 | * *  * *  *  *  *  * 5  * * * | 0 0 0 0  0 1 0 1 0
....oo5....oo&#x  |  0  0 0 0  1  1 | * *  * *  *  *  *  * * 10 * * | 0 0 0 0  0 0 1 1 0
.....x ......     |  0  0 0 0  0  2 | * *  * *  *  *  *  * *  * 5 * | 0 0 0 0  0 0 1 0 1  {5},{10}-join
...... .....x     |  0  0 0 0  0  2 | * *  * *  *  *  *  * *  * * 5 | 0 0 0 0  0 0 0 1 1  {4},{10}-join
------------------+-----------------+-------------------------------+-------------------
x.....5x.....     | 10  0 0 0  0  0 | 5 5  0 0  0  0  0  0 0  0 0 0 | 1 * * *  * * * * *  top {10}
xx.... ......&#x  |  2  2 0 0  0  0 | 1 0  2 1  0  0  0  0 0  0 0 0 | * 5 * *  * * * * *
...... xfo...&#xt |  2  2 1 0  0  0 | 0 1  2 0  2  0  0  0 0  0 0 0 | * * 5 *  * * * * *
.x.o.. ......&#x  |  0  2 0 1  0  0 | 0 0  0 1  0  2  0  0 0  0 0 0 | * * * 5  * * * * *
.oooo.5.oooo.&#xr |  0  1 1 1  1  0 | 0 0  0 0  1  1  1  1 0  0 0 0 | * * * * 10 * * * *  cycle(BCED)
...... ..o.x.&#x  |  0  0 1 0  2  0 | 0 0  0 0  0  0  2  0 1  0 0 0 | * * * *  * 5 * * *
...ofx ......&#xt |  0  0 0 1  2  2 | 0 0  0 0  0  0  0  2 0  2 1 0 | * * * *  * * 5 * *
...... ....xx&#x  |  0  0 0 0  2  2 | 0 0  0 0  0  0  0  0 1  2 0 1 | * * * *  * * * 5 *
.....x5.....x     |  0  0 0 0  0 10 | 0 0  0 0  0  0  0  0 0  0 5 5 | * * * *  * * * * 1  bottom {10}
or
o.....5o.....     & | 20  *  * |  1  1  1  0  0  0 | 1  1  1  0  0  polar, at {10}
.o....5.o....     & |  * 20  * |  0  0  1  1  1  1 | 0  1  1  1  1  tropical
..o...5..o...     & |  *  * 10 |  0  0  0  0  2  2 | 0  0  1  1  2  medial
--------------------+----------+-------------------+--------------
x..... ......     & |  2  0  0 | 10  *  *  *  *  * | 1  1  0  0  0  {4},{10}-join
...... x.....     & |  2  0  0 |  * 10  *  *  *  * | 1  0  1  0  0  {5},{10}-join
oo....5oo....&#x  & |  1  1  0 |  *  * 20  *  *  * | 0  1  1  0  0
.x.... ......     & |  0  2  0 |  *  *  * 10  *  * | 0  1  0  1  0
.oo...5.oo...&#x  & |  0  1  1 |  *  *  *  * 20  * | 0  0  1  0  1  {4},{5}-join
.o.o..5.o.o..&#x  & |  0  1  1 |  *  *  *  *  * 20 | 0  0  0  1  1  {3},{4}-join
--------------------+----------+-------------------+--------------
x.....5x.....     & | 10  0  0 |  5  5  0  0  0  0 | 2  *  *  *  *  {10}
xx.... ......&#x  & |  2  2  0 |  1  0  2  1  0  0 | * 10  *  *  *  polar {4}
...... xfo...&#xt & |  2  2  1 |  0  1  2  0  2  0 | *  * 10  *  *  {5}
.x.o.. ......&#x  & |  0  2  1 |  0  0  0  1  0  2 | *  *  * 10  *  {3}
.oooo.5.oooo.&#xr   |  0  2  2 |  0  0  0  0  2  2 | *  *  *  * 10  equatorial {4}, cycle(BCED)

© 2004-2019
top of page